2014-01-30

These saw blade curves (seen in two previous posts: here and here) are arranged to have identical midpoint and when viewed like this, the endpoints of the curves all lie on two circles. The radius of each circle is 2/5 of the curve length, and the two circles are 1/5 of the curve length apart.
Based on this fact, I could use the Pythagorean theorem to formulate a mathematical relationship between the original length L, distance d between end points and curve height h:

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Purpose of this page

When you bend a thin strip of an elastic material you get a beautifully shaped curve. What geometry does this curve follow? Please help unravel this mystery by commenting these posts!

(Upside down)Because this is a "blog", oldest posts are shown last. To get the story straight - read from bottom to top!

Type of bending

I'm looking at the type of bending that is elastic (not plastic), meaning the material will spring back to its original shape when the force is released. Most materials break or deform permanently before they can reach an 'elastic and beautiful curve', but I think all 'elastic deformation' follow the same principals and therefore the same geometry.